Research On The Three-dimensional Hexahedral Meshing Technique And Its Implementation

With the development of computer technology, finite element method plays more and more important roles in the fields of the science researches and engineering applications, and is used extensively to solve all kinds of practical engineering problems. The common ground of the method is to generate discrete grids system of the analyzed model. The key step of this technology is discretization of the physical domain into elementary shapes. In order to accurately approximate physical model, high quality mesh should be guaranteed. In three-dimensional finite element analysis, tetrahedron, hexahedron and hybrid mesh are used. At present, the method of tetrahedron has been fully mature. However, because of its more complex topology, there is no all-hexahedral element mesh method for any complicated three-dimensional solid model. So the generation of an all-hexahedral element mesh of complex three-dimensional solid model is always a difficult problem. But hexahedral element mesh can make the computation more efficient and thus in general is a better solution. Therefore, there are more and more researches about automatic hexahedral mesh generation in these years, and having some progress. But the algorithms about automatic hexahedral mesh generation are not robust.Because of high deformation, high accuracy and decreasing the overall element count to obtain the same level of accuracy against with tetrahedron, hexahedral mesh are widely used in three-dimensional finite element simulation and other engineering applications. Based on comprehensive investigation and study about common hexahedral element mesh algorithms and widely reading the related literature, this thesis detailing presents the existing problems and development tendency of the common hexahedral element mesh algorithms. Currently, the representative all-hexahedral mesh generation methods are:Mapping, Sub-Mapping, Sweeping, Grid-Based, Media-Surface, Plastering, Whisker Weaving, Indirect method.In addition, this paper has presented an algorithm of hexahedron mesh generation based on indirect method. This method is based on the decomposition of tetrahedron to automatically convert into non-structural hexahedral mesh, using mesh subdivision and mesh optimization to improve the quality of mesh. This thisis detailing describes the specific procedure and related algorithm. On the basis of the method, it realizes the algorithm combined with the open source software Gmsh, presents the important data structure and data file formation of the program, finally, showed examples.